Fluid densitometer with temperature sensor to provide temperature correction

ABSTRACT

A sensor for measuring a density of a fluid is provided. The sensor ( 200 ) includes a flow tube ( 104 ) for receiving the fluid and a vibration driver ( 102 ) coupled to the flow tube, the vibration driver configured to drive the flow tube to vibrate. The sensor also includes a vibration detector ( 106 ) coupled to the flow tube, the vibration detector detecting characteristics related to the vibrating flow tube, and a distributed temperature sensor ( 202 ) coupled to the flow tube, the distributed temperature sensor measuring a temperature of the flow tube as the flow tube vibrates. The sensor further includes measurement circuitry ( 110 ) coupled to the vibration detector and the distributed temperature sensor, the measurement circuitry determining a density of the fluid from the detected characteristics related to the vibrating flow tube and the measured temperature of the flow tube.

BACKGROUND

1. Technical Field

Embodiments disclosed herein generally relate to the measurement of fluid properties. In particular, the disclosed embodiments are related to measuring a fluid density with a fluid densitometer, measuring a temperature of a fluid densitometer, and providing a correction to the measured fluid density based on the measured temperature.

2. Description of Related Art

There are many instances in industrial processes and controls for handling flowing fluids where the density of the moving fluid has to be determined accurately. One particular application is in the identification of reservoir fluids flowing in a well such as in a pumpout wireline formation tester (PWFT) or logging while drilling formation tester (LWDFT) used to collect reservoir fluid samples in a well drilled for hydrocarbon exploration. The in-situ determination of fluid density under reservoir conditions is of vital importance in formation evaluation. Water often co-exists with gaseous hydrocarbons and crude oil in some common geologic formations. As such, a mixture of water, gaseous hydrocarbons, and liquid hydrocarbons is often produced by a working oil well, and the mixture is ultimately separated at a downstream location. It is often desirable to determine the amount of oil that is produced in a stream flowing from a formation. Because the amount of oil produced in the stream will influence the density of the fluid, measuring the density of the fluid can provide a reasonable estimation as to the amount of oil in the fluid.

One example of a densitometer that can be used to measure the density of an unknown process fluid is a Coriolis mass flowmeter, such as disclosed in U.S. Pat. No. 4,491,025, issued to Smith et al. A Coriolis mass flowmeter may contain two parallel conduits, each typically being a U-shaped flow tube wherein each flow tube is driven such that it oscillates about an axis causing each tube to twist about a torsional axis to produce a slight deformation and deflection of the conduit proportional to the mass flow rate of the fluid. This deformation is normally measured as a small difference between the deflection at the inlet ends of the conduits compared to the deflection at the outlet ends. Both tubes are oppositely driven such that each tube behaves as a separate tine of a tuning fork and thereby cancels any undesirable vibrations that might otherwise mask the Coriolis forces. The resonant frequency at which each flow tube oscillates depends upon its total mass, i.e. the mass of the empty tube itself plus the mass of the fluid flowing therethrough. Inasmuch as the total mass will vary as the density of the fluid flowing through the tube varies, the resonant frequency will likewise vary with any changes in density.

Another example of a densitometer is discussed in U.S. Pat. No. 4,491,009, issued to Reusch, wherein the density of an unknown fluid flowing through an oscillating flow tube is proportional to the square of the period at which the tube resonates. A further exemplary densitometer is disclosed in U.S. Pat. No. 6,378,364, by Pelletier et al., which is assigned to the same assignee as the present disclosure. Therein, a measurement device compares vibration frequencies from a sample cavity and a reference cavity to determine desired fluid properties.

However, due to the limited space in downhole applications, in most of the densitometers described above, the transmitter or driver is often located in close proximity to the receiver and may cause interference between the two components. The interference may distort the signal picked up on the receiver and cause difficulty in accurately recognizing the vibratory response of the flow tube. Thus, many of the prior art methods have used multiple flow tubes to create a reference point to cancel out external interference.

Moreover, most of the densitometers described above do not provide any correction for inaccuracies in the measured fluid density arising due to the temperature of the densitometer. Consequently, the densitometers provided above often provide inaccurate density measurements, particularly in environments having extreme or varying temperatures. Thus, there is a need for a sensor for determining a fluid density and for determining an associated temperature in order to provide a correction to the determined density based on the determined temperature.

BRIEF SUMMARY

Consistent with some embodiments, a sensor for measuring a density of a fluid. The sensor includes a flow tube for receiving the fluid and a vibration driver coupled to the flow tube, the vibration driver configured to drive the flow tube to vibrate. The sensor also includes a vibration detector coupled to the flow tube, the vibration detector detecting characteristics related to the vibrating flow tube, and a distributed temperature sensor coupled to the flow tube, the distributed temperature sensor measuring a temperature of the flow tube as the flow tube vibrates. The sensor further includes measurement circuitry coupled to the vibration detector and the distributed temperature sensor, the measurement circuitry determining a density of the fluid from the detected characteristics related to the vibrating flow tube and the measured temperature of the flow tube.

Consistent with some embodiments, there is further provided a temperature sensor for measuring a temperature of a fluid densitometer to provide temperature correction effects to a fluid density determined by the fluid densitometer. The temperature sensor includes a temperature-sensitive component attached along a length of the fluid densitometer, an excitation source coupled to the temperature-sensitive component, and measurement circuitry coupled to the temperature-sensitive component.

These and other embodiments will be described in further detail below, with reference to the following drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a device for measuring a density of a fluid according to some embodiments.

FIG. 2 is a device for measuring a density of a fluid having an associated temperature sensor according to some embodiments.

FIG. 3 is a graph illustrating a relationship between a resistivity of a copper wire and temperature.

FIG. 4 is a device for measuring a density of a fluid having an associated temperature sensor according to some embodiments.

FIG. 5 is a device for measuring a density of a fluid having an associated temperature sensor according to some embodiments.

FIG. 6 is a device for measuring a density of a fluid having an associated temperature sensor according to some embodiments.

Wherever possible, the same reference numbers are used throughout the drawings to refer to the same or like elements.

DETAILED DESCRIPTION

FIG. 1 is a device for measuring a density of a fluid according to some embodiments. As shown in FIG. 1, device 100 includes magnet 102 coupled to flow tube 104. Although device 100 only includes a single magnet, consistent with some embodiments, two or more magnets may be coupled to flow tube 104, such as disclosed in U.S. Pat. No. 6,686,176, by Pelletier et al., which is assigned to the same assignee as the present disclosure. Consistent with some embodiments, magnet 102 may be mounted on flow tube 104, and in other embodiments, magnet 102 may be spaced a predetermined distance away from flow tube 104. Coil 106 is wound around magnet 102 and is coupled to test circuitry 108, which includes measurement circuitry 110 and current source 112. Consistent with some embodiments, current source 112 provides a current pulse to coil 106. In other embodiments, current source 112 may be a direct current or alternating current source and provide a direct or alternating steady-state current to coil 106.

Device 100 also includes a rigid housing 114 and two bulkheads 116. Rigid housing 114 surrounds and protects a volume through which flow tube 104 passes and reduces the response to vibrations not associated with particular vibratory modes of flow tube 104. As shown in FIG. 1, flow tube 104 extends through bulkheads 116. Consistent with some embodiments, flow tube 104 is part of a flow line of a pumpout wireline formation tester (PWFT) or logging while drilling formation tester (LWDFT) used to collect reservoir fluid samples in a well drilled for hydrocarbon exploration, and a includes a portion enclosed in rigid housing 114 and secured by bulkheads 116 for testing. Bulkheads 116 assist in sealing the volume for measuring a fluid density and securing the flow tube 104 within that volume. The volume preferably contains air, a vacuum or a relatively inert gas such as nitrogen or argon. If gasses are used, then they are preferably at atmospheric pressure when the device is at room temperature. Rigid housing 114, bulkheads 116, and flow tube 104 are preferably made from material in a configuration that can withstand pressures of more than 20,000 psi (pounds per square inch) at temperatures of 250° C. or more. Two examples of suitable materials are Titanium and Hastaloy-HA276C. Preferably, bulkheads 116 and flow tube 104 are constructed from the same piece of material, with bulkheads 116 being regions of larger diameter on either end of flow tube 104. Alternatively, flow tube 104 may be welded to bulkheads 116, or otherwise attached. Flow tube 104 may also be secured to rigid housing 314 by o-rings or other types of elastomeric means. Preferably, rigid housing 114, bulkheads 116, and flow tube 104 are constructed from the same material in order to alleviate thermally induced stresses when the system is in thermal equilibrium.

Consistent with some embodiments, magnet 102 and coil 106 act as both a vibration source and a vibration detector. However, in other embodiments, magnet 102 and coil 106 may act as the vibration source or the detector while other components act as the other of the vibration source or detector. In such embodiments, the other of the vibration source or detector may be another magnet and coil arrangement, such as disclosed in U.S. Pat. No. 6,686,176, by Pelletier et al., which assigned to the same assignee as the present disclosure. Returning to FIG. 1, application of a current pulse from current source 112 to coil 106 generates an electromagnetic force that interacts with magnet 102 and causes flow tube 104 to vibrate. After the current pulse has been applied, the vibration in flow tube 104 moves magnet 102 within coil 106, therefore creating a voltage on coil 106. Coil 106, or other not shown vibration detector, detects this voltage as it varies over time and provides the detected voltages to measurement circuitry 110. From the provided voltages, measurement circuitry 110 calculates a fluid density of the fluid in flow tube 104. In some embodiments measurement circuitry 110 performs an operation on the provided voltages and determines a resonance frequency of flow tube 104 from the voltages. Consistent with some embodiments, the operations may include a transform which transforms a time-based voltage function representing the voltage induced in coil 106 over time to a frequency based function. The transform may be any known transform such as a discrete Fourier transform (DFT), a fast Fourier transform (FFT), or a discrete wavelet transform. The fluid density of the fluid flowing in flow tube 104 can then be calculated from the determined resonance frequency.

Further consistent with some embodiments, measurement circuitry 110 may include a spectral analyzer configured to perform a specific transform on the time-based voltage function. Alternatively, measurement circuitry 110 may include a processor configured to execute instructions stored in a memory coupled to the processor to perform a specific transform on the time-based voltage function and then execute further instructions stored in the memory to calculate a fluid density from a resonance frequency determined from the specific transform. As yet another alternative, measurement circuitry 110 may include application specific circuitry configured to perform a specific transform, determine a resonance frequency, and then determine a fluid density from the determined resonance frequency. Furthermore, measurement circuitry 110 may also include components capable of calculating further properties of the fluid, such as a viscosity of the fluid and a temperature of flow tube 104.

For example, the motion of flow tube 104 as it vibrates may be described by the following equation:

$\begin{matrix} {{{\left( {m_{T} + m_{L}} \right)\frac{\partial^{2}\psi}{\partial t^{2}}} = {{{- {EI}}\frac{\partial^{4}\psi}{\partial x^{4}}} + f_{P} + f_{T} + f_{C} + f_{V} + f_{M}}},} & (1) \end{matrix}$ where t is time, ψ is a transverse displacement of an element on flow tube 104, x is a distance of the element from one end of flow tube 104, E is an elastic modulus of flow tube, I is an area moment of inertia of flow tube 104, m_(L) is a linear density of the fluid inside flow tube 304, m_(T) is a linear density of material used to form flow tube 104, f_(P) is force on flow tube 104 due to pressure, f_(T) is additional tensile forces on flow tube 104, f_(C) is the Coriolis force, f_(V) is a force on flow tube 104 due to fluid flow, and f_(M) is an additional mass loading due to the presence of magnet 102. From detailed force analysis, it can be shown that the forces are given by:

$\begin{matrix} {{f_{P} = {{- {PA}}\frac{\partial^{2}\psi}{\partial x^{2}}}},} & (2) \\ {{f_{T} = {T\frac{\partial^{2}\psi}{\partial x^{2}}}},} & (3) \\ {{f_{C} = {{- 2}m_{L}V\frac{\partial^{2}\psi}{{\partial t}{\partial x}}}},} & (4) \\ {{f_{V} = {{- m_{L}}V^{2}\frac{\partial^{2}\psi}{{\partial t}{\partial x}}}},} & (5) \\ {{f_{M} = {M\frac{\partial^{2}\psi}{\partial t^{2}}{\delta\left( {x - x_{1}} \right)}}},} & (6) \end{matrix}$ where T is a tension in flow tube 104, V is a flow velocity of the fluid in flow tube 104, M is the mass of magnet 102, x₁ is a location of magnet 102 on flow tube 104, and δ(x−x₁) is a Dirac delta-functions at x₁. When temperature, pressure, and fluid density are known, the differential equation can be solved to yield the wave number β₀ that is related to the resonance frequency f₀ of the flow tube 104 as a function of fluid density:

$\begin{matrix} {{f_{0}(\rho)} = {\frac{\beta_{0}^{2}}{2\pi\; L^{2}}{\sqrt{\frac{{E\left( T_{t} \right)} \cdot {I\left( T_{t} \right)}}{m_{t} + m_{f}}}.}}} & (7) \end{matrix}$ This equation may then by inverted to obtain a relationship of the density of the fluid in flow tube 104 as a function of the resonance frequency f₀ of the flow tube 104. Consistent with some embodiments, measurement circuitry 110 may apply the above equations to determine a resonance frequency, and then determine a fluid density from the determined resonance frequency.

As shown in FIG. 1, magnet 102 and coil 104 are positioned along flow tube 104 such that magnet 102 is mounted on flow tube 104 at a center position along the length of flow tube 104. However, in some embodiments, magnet 102 may be mounted on or arranged to be coupled to flow tube 104 at other points along the length of flow tube 104. In such embodiments, it is preferable that magnet 102 and coil 106 be mounted near an antinode (point of maximum displacement from the equilibrium position) of the mode of vibration they are intended to excite and monitor. It is contemplated that more than one mode of vibration may be employed (e.g. the vibration source may switch between multiple frequencies to obtain information from higher resonance harmonic frequencies). The vibration sources and detectors are preferably positioned so as to be near antinodes for each of the vibration modes of interest. The locations of nodes (points of zero vibrational amplitude) and antinodes are determined by the wavelength of the vibration mode and by the mounting of flow tube 304. The frequency f and wavelength λ are related to the speed of sound v in the material by the equation v=fλ.

Although device 100 allows for the determination of a fluid density, the determined fluid density may suffer from inaccuracies relating to a temperature of flow tube 104, or even a temperature of a fluid. As is known, density varies with changing pressure and/or temperature. Thus, although device 100 may provide reasonable accuracy in ideal conditions, in environments where temperature is not ideal or is rapidly changing, the determined fluid density may be inaccurate. Moreover, device 100 determines the fluid density by first determining a resonant frequency of flow tube 104. Flow tube 104 has an associated elastic modulus depending on the material from which flow tube 104 is made, and the associated elastic modulus has a strong dependence on the temperature of the material. Furthermore, discrete temperature sensors cannot be attached to flow tube 104 due to the vibration of flow tube 104. Not only would the manufacture or attachment of a discrete temperature sensor provide difficulties in ensuring that the discrete temperature sensor remain attached while flow tube vibrates, but the attached discrete temperature sensor would also dampen the vibrations of flow tube 104 leading to inaccurate density measurements based on the resonant frequency. Consequently, there is a need for a densitometer which also measures the temperature of the densitometer to provide a correction to the determined fluid density based on the measured temperature.

FIG. 2 is a device for measuring a density of a fluid having an associated temperature sensor according to some embodiments. Device 200 shown in FIG. 2 is similar to device 100 shown in FIG. 1, so elements that remain the same will not be discussed in detail. However, device 200 differs from device 100 in that a metallic wire 202 is attached to flow tube 104 for use as a temperature sensor. In particular, metallic wire 202 is a distributed temperature sensor. Consistent with some embodiments, metallic wire 202 may be a fine metallic wire made of platinum or copper. In operation, a known current I is applied to metallic wire 202 from wire current source 204 that produces a voltage V in metallic wire 202 based on a resistance R of metallic wire. The resistance R of metallic wire 202 depends on a temperature of flow tube 104 according to a known relation or dependency. Thus, the resistance R of metallic wire 202 which, according to Ohm's Law, is proportional to the voltage V in metallic wire 202, will be at a certain level depending on the temperature of flow tube 104 and have a proportional voltage V associated therewith that can be detected by measurement circuitry 110 to determine the temperature. Moreover, the resistance R of metallic wire 202 depends on the temperature of flow tube 104 and, thus, the voltage V induced in metallic wire 202 depends on the temperature of flow tube 104. Measurement circuitry 110 includes a voltage detector and detects the voltage induced in metallic wire 202 and determines a temperature of flow tube 104 according to a known relationship between the resistance R of metallic wire 202 and the temperature of flow tube 104. For example, the resistance of a conductor can be expressed as a function of its temperature as R=R ₀[1+α(T−T ₀)]  (8), where R is a resistance of metallic wire 202, at temperature T, R₀ is a resistance of the conductor at temperature T₀, and α=temperature coefficient of resistance. By detecting a voltage induced in metallic wire 202, measurement circuitry may then determine resistance R of metallic wire 202, and use the determined resistance to calculate the temperature of flow tube 104 using equation (8). The determined temperature can then be used to apply a correction to the determined fluid density to provide a more accurate determination of the determined fluid density. Although device 200 illustrates a single magnet 102 and coil 106 arrangement as a vibration driver and vibration detector, other vibration drivers and vibration detectors may be used, such as additional magnet-coil arrangements, such as described in U.S. Pat. No. 6,686,176, by Pelletier et al., which is assigned to the same assignee as the present disclosure.

According to some embodiments, metallic wire 202 may be used as a vibration detector and further used to determine a density of fluid in flow tube 104. In a manner similar to determining a temperature of flow tube 104, a known current I is applied to metallic wire 202 from wire current source 204 that produces a voltage V in metallic wire 202 based on a resistance R of metallic wire. As flow tube 104 vibrates, it also bends, which creates mechanical stress along the length of flow tube 104. This created mechanical stress produces variations in resistance R of metallic wire 202 which, according to Ohm's Law, will also create voltage variations in metallic wire 202. The voltage variations are detected by measurement circuitry 110 and used to calculate a resonance frequency in the same way as discussed above with respect to FIG. 1. Thus, the detected voltage of metallic wire 202 may be used to determine a temperature of tube 104 and a fluid density of a fluid in flow tube 104.

FIG. 3 is a graph illustrating a relationship between a resistivity of a copper wire and temperature. As discussed above, in some embodiments metallic wire 202 may be a copper wire. As shown in FIG. 3, the resistance R of a copper wire has a linear temperature dependence. Thus, by determining a resistance R of a copper wire, a temperature of the copper wire may be determined. Similar temperature dependencies exist for other wire materials as well. Consequently, device 200 can determine a temperature of metallic wire 202 and, thus, a temperature of flow tube 104, by determining a voltage V on metallic wire 202 induced by a known current I. The determined voltage V can then be used with the known current I to determine a resistance R of metallic wire 202 and the determined resistance R can be used to determine a temperature of metallic wire 202 based on a known relationship or dependence between the resistance R of metallic wire 202 and temperature, such as the relationship shown in FIG. 3.

FIG. 4 is a device for measuring a density of a fluid according to some embodiments. Device 400 shown in FIG. 4 is similar to device 200 shown in FIG. 2, so elements that remain the same will not be discussed in detail. However, device 400 differs from device 200 in that strain gauge 402 is used as a temperature sensor. Consistent with some embodiments, strain gauge 402 may be an insulator material 404 deposited along a length of flow tube 104 and a metallic or semiconducting material 406 deposited over insulator material 404. Insulator material 404 and metallic or semiconducting material 406 may be deposited on flow tube 104 using known deposition methods. In operation, a known current I is applied to strain gauge 402 from strain gauge current source 408 that produces a voltage V in metallic or semiconductor material 406 based on a resistance R of metallic or semiconductor material 406. Metallic or semiconductor material 406 is chosen such that it has a known relationship between its resistance R and its temperature. The voltage across metallic or semiconductor material is detected by a voltage detector in measurement circuitry 110 and used to determine its resistance R from the known current I. Based on the known relationship between its resistance R and temperature, measurement circuitry 110 calculates a temperature in the same way as discussed above with respect to FIGS. 2 and 3.

According to some embodiments, strain gauge 402 may be used as a vibration detector and further used to determine a density of fluid in flow tube 104. In a manner similar to determining a temperature of flow tube 104, a known current I is applied to strain gauge 402 from wire current source 404 that produces a voltage V in strain gauge 402 based on a resistance R of strain gauge 402. As flow tube 104 vibrates, it also bends, which creates mechanical stress along the length of flow tube 104. This created mechanical stress produces variations in resistance R of strain gauge 402 which, according to Ohm's Law, will also create voltage variations in strain gauge 402. The voltage variations are detected by measurement circuitry 110 and used to calculate a resonance frequency in the same way as discussed above with respect to FIG. 1. Thus, the detected voltage of strain gauge 402 may be used to determine a temperature of tube 104 and a fluid density of a fluid in flow tube 104.

FIG. 5 is a device for measuring a density of a fluid according to some embodiments. Device 500 shown in FIG. 5 is similar to device 200 shown in FIG. 2, so elements that remain the same will not be discussed in detail. However, device 500 differs from device 200 in that fiber optic sensor 502 is used as a temperature sensor. Consistent with some embodiments, fiber optic sensor 502 may be a fiber Bragg grating, which includes the fiber optic core 504 surrounded by the fiber optic cladding material 506 with at least one Bragg grating 508 enclosed in a portion of fiber optic core 504. When a light pulse propagates along fiber optic sensor 502, the light pulse interacts with materials of fiber optic sensor quantum mechanically to produce two types of Raman scattering: Stokes scattering and anti-Stokes scattering. Stokes scattering is independent of temperature, but anti-Stokes scattering latter is temperature-dependent. By measuring the ratio of intensity of the anti-Stokes scattering to Stokes scattering, a local temperature of fiber optic sensor 502 and thus, flow tube 104 may be determined via the following equation:

$\begin{matrix} {{{R(T)} = {\left( \frac{v_{a}}{v_{s}} \right)^{4}{\exp\left( {- \frac{hv}{k_{B}T}} \right)}}},} & (9) \end{matrix}$ where ν is the frequency of the incident light, ν_(a) is the frequency of the anti-Stokes scattered light, ν_(s) is the frequency of the Stokes scattered light, T is absolute temperature, and h and k_(B) are respectively the well known the Plank constant and Boltzmann constant. Thus fiber optic sensor 502 may be used to determine a temperature of flow tube 104.

According to some embodiments, fiber optic sensor 502 may be used as a vibration detector and further used to determine a density of fluid in flow tube 104. In a manner similar to determining a temperature of flow tube 104, as flow tube 104 vibrates, it also bends which creates mechanical stress along the length of flow tube 104. This created mechanical stress will influence the effective refractive index η_(eff) of Bragg grating 508 and thus produce changes in the light that is transmitted through fiber optic sensor 502 from light source 510. Consequently, measurement circuitry 110 may include an optical sensor that is able to detect these changes and use the changes of light to determine the mechanical stress of flow tube 104 from the vibration of flow tube 104 to determine a resonance frequency of flow tube 104. The density of the fluid flowing through flow tube 104 may then be determined from the determined resonance frequency. Thus, fiber optic sensor 502 may be used to determine a temperature of tube 104 and a fluid density of a fluid in flow tube 104.

FIG. 6 is a device for measuring a density of a fluid according to some embodiments. Device 600 shown in FIG. 6 is similar to device 200 shown in FIG. 2, so elements that remain the same will not be discussed in detail. However, device 600 differs from device 200 in that metallic wire 202 is wrapped around flow tube 104. Consistent with some embodiments, metallic wire 202 may be a fine metallic wire made of platinum or copper. In other embodiments, strain gauge 402 or fiber optic sensor 502 may be substituted for metallic wire 202 and be wrapped around flow tube 104. In operation, a known current I is applied to metallic wire 202 from wire current source 204 that produces a voltage V in metallic wire 202 based on a resistance R of metallic wire. The resistance R of metallic wire 202 depends on a temperature of flow tube 104 according to a known relation or dependency. Thus, the resistance R of metallic wire 202 which, according to Ohm's Law, is proportional to the voltage V in metallic wire 202, will be at a certain level depending on the temperature of flow tube 104 and have a proportional voltage V associated therewith that can be detected by measurement circuitry 110 to determine the temperature. Moreover, the resistance R of metallic wire 202 depends on the temperature of flow tube 104 and, thus, the voltage V induced in metallic wire 202 also depends on the temperature of flow tube 104. The voltage is detected by a voltage detector in measurement circuitry 110 and used to determine a temperature of flow tube 104 according to a known relationship between metallic wire 202 and the temperature of flow tube 104. When using strain gauge 402 or optic sensor 502 instead of metallic wire 202, the operation will be as is discussed in FIGS. 4 and 5 respectively. Furthermore, metallic wire 202, strain gauge 402, and optic sensor 502 may also be used to determine a fluid density from a vibration of flow tube 104 as is discussed above with respect to FIGS. 2, 4, and 5.

Consistent with some embodiments, using metallic wire 202 (or strain gauge 402 or optic sensor 502) wrapped around flow tube 104, the hoop stress of flow tube 104 may be determined. Under a pressure P, a flow tube such as flow tube 104, with inner radius b and outer radius a will experience expansion in its outer radius by

$\begin{matrix} {{{\Delta\; a} = \frac{{Pb}^{2}\left( {2 - v} \right)}{E\left( {a^{2} - b^{2}} \right)}},} & (10) \end{matrix}$ where E is the elastic modulus of flow tube 104, and v is the Poisson's ratio of flow tube 104. The change in radius Δa results in a change in the outer circumference (2πa) of the tube which in turn results in minute change in the resistance R of metallic wire 202 wrapped around flow tube 104. This resistance change ΔR may then be measured using well known methods, such as using a quarter-bridge Wheatstone bridge composed of metallic wire 202 and three dummy resistors and excited by a voltage V_(br), such that the strain ε from pressure P may be determined by

${ɛ = \frac{\Delta\; R}{SR}},$ where S is a strain sensitivity factor determined by the material of metallic wire 202. Because the strain ε may be equal to

$\frac{\Delta\; a}{a},$ knowing the strain ε from pressure P and the change in radius Δa, the pressure P from the fluid in flow tube 104 can be determined using equation (10). Once the pressure P is determined, measurement circuitry 110 may then determine the hoop stress σ_(θ) of flow tube 104 using the equation

${\sigma_{\theta} = \frac{P \cdot r}{t}},$ where P is the internal pressure from the fluid, t is the thickness of the wall of flow tube 104, and r is the radius of flow tube 104.

Consequently, embodiments described herein provide improvements in the design of fluid densitometers. For example, embodiments described herein use a distributed temperature sensor attached to the densitometer to measure a temperature of the densitometer to provide a temperature correction to a fluid density measured by the densitometer. Other embodiments described herein provide a densitometer wherein the components used to measure the temperature are also used in determining the fluid density. Other embodiments provide a densitometer capable of measuring not only the density of the fluid, but also a pressure of the fluid and a temperature of the densitometer, using the same components. Embodiments described herein are exemplary only. One skilled in the art may recognize various alternative embodiments from those specifically disclosed. Those alternative embodiments are also intended to be within the scope of this disclosure. As such, the embodiments are limited only by the following claims. 

We claim:
 1. A sensor for measuring a density of a fluid, comprising: a flow tube for receiving the fluid; a vibration driver coupled to the flow tube to drive the flow tube to vibrate; a vibration detector coupled to the flow tube, the vibration detector detecting characteristics related to the vibrating flow tube; a distributed optical temperature sensor extending along a length of the flow tube and coupled thereto, the distributed optical temperature sensor having a plurality of gratings distributed along a length of the distributed optical temperature sensor, each grating being used to measure a local temperature along the flow tube as the flow tube vibrates; and measurement circuitry coupled to the vibration detector and the distributed optical temperature sensor, the measurement circuitry determining a density of the fluid from the detected characteristics related to the vibrating flow tube and the measured temperature of the flow tube.
 2. The sensor of claim 1, wherein the distributed optical temperature sensor comprises: a optical fiber coupled to the flow tube and to the measurement circuitry, the optical fiber comprising a cladding surrounding a core, and a plurality of distributed Bragg gratings formed in the core; and a light source coupled to the optical fiber and providing light through the optical fiber, wherein: properties of the light through the optical fiber change in response to a mechanical stress caused by the vibration of the flow tube; and the measurement circuitry detects the changing light properties and determines a temperature of the flow tube.
 3. The sensor of claim 1, wherein: the distributed optical temperature sensor is wrapped around the flow tube and measures a hoop stress of the flow tube in addition to the temperature of the flow tube; and the measurement circuitry determines a pressure of the fluid in the flow tube from the measured hoop stress.
 4. The sensor of claim 1, further comprising: a first bulkhead secured to a first end of the flow tube; a second bulkhead secured to a second end of the flow tube; and a rigid housing surrounding the flow tube, wherein the vibration driver is a magnet having a coil wound there around to drive the flow tube to vibrate, the magnet and coil being positioned along the flow tube near an antinode of a vibration mode, and wherein the distributed optical temperature sensor acts as the vibration detector, thereby measuring the temperature of the flow tube and detecting the characteristics related to the vibrating fluid flow.
 5. A temperature sensor for measuring a temperature of a fluid densitometer to provide temperature correction effects to a fluid density determined by the fluid densitometer, the temperature sensor comprising: a temperature-sensitive optical component extending along a length of the fluid densitometer, the temperature-sensitive optical component having a plurality of gratings distributed along a length of the temperature-sensitive optical component, each grating being used to measure a local temperature along the fluid densitometer; an excitation source coupled to the temperature-sensitive component; and measurement circuitry coupled to the temperature-sensitive component.
 6. The temperature sensor of claim 5, wherein: the measurement circuitry comprises an optical detector; the temperature-sensitive optical component comprises a optical fiber coupled to the flow tube and to the measurement circuitry, the optical fiber comprising a cladding surrounding a core, and a plurality of distributed Bragg gratings formed in the core; the excitation source comprises a light source coupled to the optical fiber and providing light through the optical fiber, wherein: properties of the light provided through the optical fiber depend on the temperature of the fluid densitometer; and the optical detector detects the light properties.
 7. The temperature sensor of claim 6, wherein the measurement circuitry determines the temperature of the fluid densitometer from the detected light properties.
 8. The sensor of claim 5, wherein: the temperature-sensitive optical component is wrapped around the fluid densitometer and measures a hoop stress of the fluid densitometer in addition to the temperature of the fluid densitometer; and the measurement circuitry determines a pressure of a fluid in the fluid densitometer from the measured hoop stress.
 9. The sensor of claim 5, wherein the temperature-sensitive optical component measures properties related to a density of a fluid.
 10. The sensor of claim 5, wherein the temperature-sensitive optical component detects vibration of the fluid densitometer, thereby detecting characteristics related to vibrating fluid flow. 